Question: Simplify the following expression: $t = \dfrac{35z}{-45z^2 + 40z}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $35z = (5\cdot7 \cdot z)$ The denominator can be factored: $-45z^2 + 40z = - (3\cdot3\cdot5 \cdot z \cdot z) + (2\cdot2\cdot2\cdot5 \cdot z)$ The greatest common factor of all the terms is $5z$ Factoring out $5z$ gives us: $t = \dfrac{(5z)(7)}{(5z)(-9z + 8)}$ Dividing both the numerator and denominator by $5z$ gives: $t = \dfrac{7}{-9z + 8}$